How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given $y=x^4+2x^2+1$ ?

Question

1597 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-01T16:49:20

$y_("intercept")=1$

No x-intercept.

Set $X=x^2$ giving:

$y=X^2+2X+1$

$y=(X+1)^2$

$+-(X+1)=sqrt(y)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(blue)("Determine x intercept")$

Set $y=0$

$-X-1=0 => x^2=-1$

$x=+-sqrt(-1)" "->" "x=+-i$

$color(green)("Thus there is no "x_("intercept"))$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(blue)("Determine y intercept")$

$y_("intercept")$ occurs at $X=0$

$y=X^2+2X+1" "->" "y=0^2+2(0)+1 = 1$

$color(green)(y_("intercept")=1$
Tony B

How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given y=x^4+2x^2+1y=x^4+2x^2+1?